An Overpartition Companion of Andrews and Keith's 2-colored $q$-series Identity
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916468071858176 |
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| author | Waldron, Hunter |
| author_facet | Waldron, Hunter |
| contents | Andrews and Keith recently produced a general Schmidt type partition theorem using a novel interpretation of Stockhofe's bijection, which they used to find new $q$-series identities. This includes an identity for a trivariate 2-colored partition generating function. In this paper, their Schmidt type theorem is further generalized akin to how Franklin classically extended Glaisher's theorem. As a consequence, we obtain a companion to Andrews and Keith's 2-colored identity for overpartitions. These identities appear to be special cases of a much more general result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Overpartition Companion of Andrews and Keith's 2-colored $q$-series Identity Waldron, Hunter Combinatorics Andrews and Keith recently produced a general Schmidt type partition theorem using a novel interpretation of Stockhofe's bijection, which they used to find new $q$-series identities. This includes an identity for a trivariate 2-colored partition generating function. In this paper, their Schmidt type theorem is further generalized akin to how Franklin classically extended Glaisher's theorem. As a consequence, we obtain a companion to Andrews and Keith's 2-colored identity for overpartitions. These identities appear to be special cases of a much more general result. |
| title | An Overpartition Companion of Andrews and Keith's 2-colored $q$-series Identity |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.16215 |